Low lying fog bounding object rendering as solid
As an alternative to smoke you can use volume scattering.

In an example like this:



Add a mesh that uses a volume scatter node as the volume.



Using a gradient and a color ramp you can control the height and density of the fog.



Using additional textures to affect the transparency of the volume scattering you can get a less homogeneous mist.



To move the fog animate the mapping used on the textures.





Here's the file: